On financial markets, Brownian-based models have been the most widely used since the establishment of the Black and Scholes framework. These models require numerous calibrations, and their performance is sufficient as long as the data is low frequency (i.e., a few data per day). Over the last decade, with the arrival of high-frequency data, such models have no longer been able to report market observations. Researchers have thus begun looking for new methods. The most promising new path involves building models based on fractional stochastic volatility. This supposes that volatility fluctuation is driven by fractionary Brownian motion, thus introducing memory, correlation and roughness properties.

The question remains as to what these models can do: how to calculate prices, how to create a hedging strategy or how to build a replicating portfolio.